Clearly mark answers to the multiple choice problems on your paper and your scantron.
1. [5 pts] Find the limit, if it exists for
lim
x 2
3

x  2
 1.
(a) - 1
(b) 1
(c)

(d)  
(e) none of these
______________________________________________________________________________________
2. [5 pts] Find the limit, if it exists for
(a) 1
(b)
4
7
(c) d.n.e.
(d) 0
(e) none of these
lim
x  1
x
x
2
 2x  3
2
 5x  6
.
3. [5 pts] How long will it take a population of 25 bacteria to triple at a growth rate of 5%?
(a) t 
ln 3
. 05
(b) t 
ln 3
5
(c)
t 
 3 
ln 

 25 
. 05
(d)
t 
 3 
ln 

 25 
5
(e) none of these
______________________________________________________________________________________
4. [5 pts] Find all points at which
(a) (   ,  1 )  (  1, 0 )
(b) (  1, 0 )  ( 0 , 1 )
(c) ( 0 , 1)  ( 1,  )
(d) (   ,  1)  ( 1,  )
(e) none of these
ln (1  x )
ln (1  x )
is continuous.
5. [5 pts] Find a value c so that the following function is continuous for all values of x:

1  x , x  2
f (x)  

 cx  1 , x  2
2
(a) 0
(b) 1
(c) - 1
(d) 2
(e) none of these
_____________________________________________________________________________________
6. [5 pts] Which of the following functions corresponds with the semilog graph below.
(a) y 
1
x  1
(b) y 
2
1
log x
2
(d)
y 
1
10

10

x
(e) none of these
(c)
y  10
x
2

1
10
7. [5 pts] Find the limit, if it exists for
lim
4 cos x  4  3 sin x
x 0
(a)
.
5x
3
5
(b)
4
5
(c) 
4
5
(d)
0
(e) none of these
_______________________________________________________________________________________
8. [5 pts] Find the limit, if it exists for
(a) - 1
(b) 1
(c)

(d)  
(e) none of these
lim
x  
x
2
1  x
.
9. [5 pts] Use a logarithmic transformation to find a linear relationship between appropriate transformations of
x and y if y  4 x 5 .
(a) log y  4 x  log 5
(b) log y  5 x  log 4
(c) log y  5 log x  log 4
(d) log y  4 log x  log 5
(e) none of these
_________________________________________________________________________________________
10. [5 pts] Let
f (x)  x
4
 x
3
 x  1.
Using the Intermediate Value Theorem and the Bisection Method,
what is the smallest interval on which we can conclude that f ( x ) has a root?
(a) (- 1, 0)
(b) (0, 1)

(c)  0 ,

1

2
1

, 0
2

(d) 
(e) none of these
11. [10 pts.] (a) Graph f ( x )  e x and show that it is one to one. Graph f ( x )  ln x and show
algebraically that it is the inverse of f ( x )  e x . List the domain and range of each function.
(b) Solve log ( x 2  1)  log ( x  1)  1
(a)
12. [10 pts.] Given
f (x) 
1

 1 , x 2

(
x

3
)


2 ,
x  2

,
definition of continuity if f ( x ) is continuous at x = 2.
carefully graph f ( x ) and determine by the 3 step
13. [5 pts. each] Compute each of the following limits.
(a)
lim
2x
2
x  0
(b)
lim
x  0
e


 

 10 
cos 

 x 
 1


x

1
x  1
14. Given the doublelog plot below, find a functional relationship between x and y.
15. [10 pts] (a) Use the limit definition of the derivative to find f  ( x ) for f ( x ) 
(b) Find the equation of the tangent to f ( x ) 
2x  1
at x = 1.
2x  1
.
MATH 147
EXAM I
NAME ___________________________________________
SECTION # _______________
SEAT # ____________
Clearly mark answers to the multiple choice problems on your paper and your scantron.
In order to obtain full credit for partial credit problems, all work must be shown. Credit will not
be given for an answer not supported by work.
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